Scatter plots ppt
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This document discusses finding the line of best fit for scatter plot data using a graphing calculator. It explains that a line of best fit shows the relationship between two sets of data using linear regression. The calculator computes the equation of the line of best fit as y=ax+b and provides the correlation coefficient r, which indicates the strength and direction of the relationship. It includes an example of finding the line of best fit for calories and fat in fast food meals.
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Lesson 6 coefficient of determination
The document provides information about regression analysis and calculating the coefficient of determination. It includes:
1) Instructions on how to perform a regression analysis using a calculator to find the least squares regression line, correlation coefficient, and residual plot from sample data.
2) An explanation of the coefficient of determination as a measure of how much variability in the variable y can be explained by its linear relationship with variable x.
3) A calculation example finding the coefficient of determination to be 0.83 for a dataset relating height and shoe size, meaning approximately 83% of the variation in shoe size can be explained by height.
Simple Regression Years with Midwest and Shelf Space Winter .docx
Simple Regression Years with Midwest and Shelf Space Winter 2016 Page 1
Lecture Notes for Simple Linear Regression
Problem Definition: Midwest Insurance wants to develop a model able to predict sales
according to time with the company.
Results for: MIDWEST.MTW
Data Display
Row Sales Years with Midwest xy y2 x2
1 487 3 1461 237169 9
2 445 5 2225 198025 25
3 272 2 544 73984 4
4 641 8 5128 410881 64
5 187 2 374 34969 4
6 440 6 2640 193600 36
7 346 7 2422 119716 49
8 238 1 238 56644 1
9 312 4 1248 97344 16
10 269 2 538 72361 4
11 655 9 5895 429025 81
12 563 6 3378 316969 36
y=4855 x=55 xy=26,091 y
2
=2,240,687 x
2
=329
(x)
2
= 3025
(y)
2
= 23571025
Scatterplot of Midwest Data
Graphs>Scatterplot
Years with Midwest
S
a
le
s
9876543210
700
600
500
400
300
200
Scatterplot of Sales vs Years with Midwest
Evaluate the bivariate graph to determine whether a linear relationship exists and the
nature of the relationship. What happens to y as x increases? What type of relationship do
you see?
Simple Regression Years with Midwest and Shelf Space Winter 2016 Page 2
Dialog box for developing correlation coefficient
Explore Linearity of Relationship for significance using t distribution
Pearson Product Moment
Correlation Coefficient
Stat>Basic Stat>Correlation
Correlations: Sales, Years with Midwest – Minitab readout
Pearson correlation of Sales and Years with Midwest = 0.833
P-Value = 0.001
Formula for computing correlation coefficient
2222
yynxxn
yxxyn
r
Hypothesis for t test for significant correlation
H0: =0
H1: ≠0
Decision Rule: Pvalue and critical ratio/critical value technique
Critical Ratio of t
t=
r
r
n
1
2
2
Conclusion:
Interpretation:
Simple Regression Years with Midwest and Shelf Space Winter 2016 Page 3
Simple linear regression assumes that the relationship between the dependent, y
and independent variable, x can be approximated by a straight line.
Population or Deterministic Model – For each x there is an exact value for y.
y = 0 + 1(x) +
y - value of independent variable
(x) - value of independent variable
0 - Value of population y intercept
1 - Slope of population regression line
- Epsilon represents the difference between y and y’. Epsilon also accounts for the independent
variables that affect y but are not in the model. (The .
2.6b scatter plots and lines of best fit
This document provides instructions for using a graphing calculator to perform linear regression on a dataset and find the line of best fit. It describes entering paired x and y data values into separate lists, using the LinReg(ax+b) function to determine the regression equation, optionally creating a scatter plot of the original data and regression line, and using the line equation to forecast values. As an example, it analyzes a dataset of alternative-fueled vehicles in the US from 1997 to predict the number in 2014.
Regression
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http://www.youtube.com/onlineteaching
Chapter 10: Correlation and Regression
10.2: Regression
Curve_Fitting.pdf
Economics
Curve Fitting
macroeconomics
Curve fitting helps in capturing the trend in the data by assigning a single function
across the entire range.
If the functional relationship between the two quantities being graphed is known to be
within additive or multiplicative constants, it is common practice to transform the data in
such a way that the resulting line is a straight line.(by plotting) A process of quantitatively
estimating the trend of the outcomes, also known as regression or curve fitting, therefore
becomes necessary.
For a series of data, curve fitting is used to find the best fit curve. The produced equation is
used to find points anywhere along the curve. It also uses interpolation (exact fit to the data)
and smoothing.
Some people also refer it as regression analysis instead of curve fitting. The curve fitting
process fits equations of approximating curves to the raw field data. Nevertheless, for a
given set of data, the fitting curves of a given type are generally NOT unique.
Smoothing of the curve eliminates components like seasonal, cyclical and random
variations. Thus, a curve with a minimal deviation from all data points is desired. This
best-fitting curve can be obtained by the method of least squares.
What is curve fitting Curve fitting?
Curve fitting is the process of constructing a curve, or mathematical functions, which possess closest
proximity to the series of data. By the curve fitting we can mathematically construct the functional
relationship between the observed fact and parameter values, etc. It is highly effective in mathematical
modelling some natural processes.
What is a fitting model?
A fit model (sometimes fitting model) is a person who is used by a fashion designer or
clothing manufacturer to check the fit, drape and visual appearance of a design on a
'real' human being, effectively acting as a live mannequin.
What is a model fit statistics?
The goodness of fit of a statistical model describes how well it fits a set of
observations. Measures of goodness of fit typically summarize the discrepancy
between observed values and the values expected under the model in question.
What is a commercial model?
Commercial modeling is a more generalized type of modeling. There are high
fashion models, and then there are commercial models. ... They can model for
television, commercials, websites, magazines, newspapers, billboards and any other
type of advertisement. Most people who tell you they are models are “commercial”
models.
What is the exponential growth curve?
Growth of a system in which the amount being added to the system is proportional to the
amount already present: the bigger the system is, the greater the increase. ( See geometric
progression.) Note : In everyday speech, exponential growth means runaway expansion, such
as in population growth.
Why is population exponential?
Exponential population growth: When resources are unlimited, populations
exhibit exponential growth, resulting in a J-shaped curve.
Line of best fit slideshare
This document provides instructions for determining a line of best fit using a graphing calculator. It outlines the 3 steps to plot points: 1) turn on plot 1, 2) enter data under L1 and L2, 3) adjust the window. Students are instructed to enter sample data, select the LinReg function to calculate the line of best fit equation, and round coefficients to three decimal places to write the line of best fit as y=ax+b. An example line of best fit equation y=0.240x-400.989 is given.
How to combine interpolation and regression graphs in R
This is a general tutorial that shows you how to take Census data, aggregate columns/rows and use interpolation lines and regression curves in your graphs. You can graph individual rows/columns or aggregate rows/columns. There is an example of graphs created here: https://www.linkedin.com/pulse/comparison-annual-income-going-back-from-2017-doug-loqa-doug-loqa/
Simple linear regression
Simple Regression presentation is a
partial fulfillment to the requirement in PA 297 Research for Public Administrators, presented by Atty. Gayam , Dr. Cabling and Mr. Cagampang
Barisan dan deret 1 bilingual
The document discusses the concepts of sequences and series in mathematics. It begins by defining an arithmetic sequence as a sequence where the difference between consecutive terms is constant. The general form of an arithmetic sequence is given as U1, U2, U3, ..., Un where Un = a + (n-1)b, with a as the first term and b as the common difference. It further explains that the sum of terms in an arithmetic sequence is called an arithmetic series. An example is worked through to find the formula for the n-th term and a specific term in a given arithmetic sequence. Sigma notation for writing sequences and series is also introduced.
Chapter5
This document summarizes bivariate data and linear regression analysis. It introduces scatterplots and the Pearson correlation coefficient as ways to examine relationships between two variables. A positive correlation indicates that as one variable increases, so does the other, while a negative correlation means one variable increases as the other decreases. The least squares line provides the best fit linear relationship between two variables by minimizing the sum of squared residuals. Calculating the slope and y-intercept of this line allows predicting y-values from x-values. Examples using bus fare and distance data demonstrate these concepts.
Simple linear regression
1) The document discusses simple linear regression using a scatter diagram and data from a study of employees' years of working experience and income.
2) It presents the scatter diagram and shows how to draw a trend line to roughly estimate dependent variable (income) values from the independent variable (years experience).
3) Equations for the least squares linear regression line are provided, including how to calculate the standard error of estimate, which is interpreted as the standard deviation around the regression line.
Mathematics TAKS Exit Level Review
This PowerPoint was created to help out graduating seniors who are taking the TAKS Mathematics Exit-Level test. It includes formulas, rules & things that they need to remember to pass the test.
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QR 1 Lesson Notes 8 - Motivation for Modelling with Linear Functions PP Show
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Chapter 16
This chapter discusses time series analysis and forecasting. The key components are:
1. A time series contains data recorded over time and can be analyzed to identify trends and patterns that may continue in the future.
2. The components of a time series are secular trends, cyclical variation, seasonal variation, and irregular variation.
3. Moving averages and weighted moving averages can be used to smooth time series data and identify trends. Linear and nonlinear trend lines can also model trends in the data.
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Have you ever wonder how Excel sets the upper limit and the lower limit on th...
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In my own case, I have not, until one day I found an obvious mistake on Excel’s dual vertical axes chart.
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- 1. Line of Best Fit line of best fit - The trend line that shows the relationship between two sets of data most A graphing calculator computes the equation of a line of best fit using a method called linear regression. The graphing calculator gives you the correlation coefficient r. -1 0 1 negative correlation no correlation positive correlation
- 2. Finding the Equation of Line of Best Fit Example: Find the line of best fit using your calculator. Show a scatter plot for the given data using your calculator. Fat(g) 6 7 10 19 20 27 36 Calories 276 260 220 388 430 550 633 Calories and Fat in Selected Fast-Food Meals
- 3. Cont (example)... Step 1. Use the EDIT feature of the STAT screen on your graphing calculator. Enter the data for fat (L1) and the data for Calories (L2) Calories and Fat in Selected Fast-Food Meals Fat(g) 6 7 10 19 20 27 36 Calories 276 260 220 388 430 550 633
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- 5. Finding the Equation of Line of Best Fit You try! Use a graphing calculator to find the equation of the line of best fit for the data at the right. What is the correlation coefficient? Year Dollars (Billions) 1993 340 1994 369 1995 402 1996 430 1997 457 1998 489 1999 527 2000 574 Recreation Expenditures Answers: y = 32.33x - 2671.67 r = 0.9964509708 Let 1993 = 93
- 6. Finding the Equation of Line of Best Fit You try! Use a graphing calculator to find the equation of the line of best fit for the data at the right. What is the correlation coefficient? Year Dollars (Billions) 1993 340 1994 369 1995 402 1996 430 1997 457 1998 489 1999 527 2000 574 Recreation Expenditures Answers: y = 32.33x - 2671.67 r = 0.9964509708 Let 1993 = 93